"""simple docstring"""


# We ignore warnings about stepping the scheduler since we step it ourselves during gradient accumulation

import warnings

from .state import AcceleratorState, GradientState


warnings.filterwarnings('ignore', category=UserWarning, module='torch.optim.lr_scheduler')






class   __UpperCAmelCase		:

				def __init__( self      ,					_lowerCamelCase      ,					_lowerCamelCase      ,					_lowerCamelCase = True      ,					_lowerCamelCase = False ):
										lowerCamelCase__   =scheduler
										lowerCamelCase__   =optimizers if isinstance(_lowerCamelCase      ,					(list, tuple) ) else [optimizers]
										lowerCamelCase__   =split_batches
										lowerCamelCase__   =step_with_optimizer
										lowerCamelCase__   =GradientState()

				def 						_a      ( self      ,					*_lowerCamelCase      ,					**_lowerCamelCase ):
										if not self.step_with_optimizer:
																# No link between scheduler and optimizer -> just step
																self.scheduler.step(*_lowerCamelCase      ,					**_lowerCamelCase )
																return

										# Otherwise, first make sure the optimizer was stepped.
										if not self.gradient_state.sync_gradients:
																if self.gradient_state.adjust_scheduler:
																						self.scheduler._step_count += 1
																return

										for opt in self.optimizers:
																if opt.step_was_skipped:
																						return
										if self.split_batches:
																# Split batches -> the training dataloader batch size is not changed so one step per training step
																self.scheduler.step(*_lowerCamelCase      ,					**_lowerCamelCase )
										else:
																# Otherwise the training dataloader batch size was multiplied by `num_processes`, so we need to do
																# num_processes steps per training step
																lowerCamelCase__   =AcceleratorState().num_processes
																for _ in range(_lowerCamelCase ):
																						# Special case when using OneCycle and `drop_last` was not used
																						if hasattr(self.scheduler      ,					"total_steps" ):
																												if self.scheduler._step_count <= self.scheduler.total_steps:
																																		self.scheduler.step(*_lowerCamelCase      ,					**_lowerCamelCase )
																						else:
																												self.scheduler.step(*_lowerCamelCase      ,					**_lowerCamelCase )

				def 						_a      ( self ):
										return self.scheduler.get_last_lr()

				def 						_a      ( self ):
										return self.scheduler.state_dict()

				def 						_a      ( self      ,					_lowerCamelCase ):
										self.scheduler.load_state_dict(_lowerCamelCase )

				def 						_a      ( self ):
										return self.scheduler.get_lr()






				def 						_a      ( self      ,					*_lowerCamelCase      ,					**_lowerCamelCase ):
										return self.scheduler.print_lr(*_lowerCamelCase      ,					**_lowerCamelCase )



"""simple docstring"""


from collections.abc import Callable
from math import pi, sqrt
from random import uniform
from statistics import mean





def      lowerCamelCase_					(   __lowerCAmelCase							)				->   List[Any]:




						'''simple docstring'''



						def is_in_circle(__lowerCAmelCase  ,       __lowerCAmelCase							) -> bool:
												lowerCamelCase__   =sqrt((x**2) + (y**2)							)
												# Our circle has a radius of 1, so a distance
												# greater than 1 would land outside the circle.
												return distance_from_centre <= 1

						# The proportion of guesses that landed in the circle
						lowerCamelCase__   =mean(
						    int(is_in_circle(uniform(-1.0  ,       1.0							)  ,       uniform(-1.0  ,       1.0							)							)							)
						    for _ in range(__lowerCAmelCase							)							)
						# The ratio of the area for circle to square is pi/4.
						lowerCamelCase__   =proportion * 4
						print(F'''The estimated value of pi is {pi_estimate}'''							)
						print(F'''The numpy value of pi is {pi}'''							)
						print(F'''The total error is {abs(pi - pi_estimate							)}'''							)





def      lowerCamelCase_					(   __lowerCAmelCase  ,       __lowerCAmelCase  ,       __lowerCAmelCase = 0.0  ,       __lowerCAmelCase = 1.0  ,       )				->   float:




						'''simple docstring'''



						return mean(
						    function_to_integrate(uniform(__lowerCAmelCase  ,       __lowerCAmelCase							)							) for _ in range(__lowerCAmelCase							)							) * (max_value - min_value)





def      lowerCamelCase_					(   __lowerCAmelCase  ,       __lowerCAmelCase = 0.0  ,       __lowerCAmelCase = 1.0							)				->   None:




						'''simple docstring'''



						def identity_function(__lowerCAmelCase							) -> float:
												return x

						lowerCamelCase__   =area_under_curve_estimator(
						    __lowerCAmelCase  ,       __lowerCAmelCase  ,       __lowerCAmelCase  ,       __lowerCAmelCase							)
						lowerCamelCase__   =(max_value * max_value - min_value * min_value) / 2

						print("******************"							)
						print(F'''Estimating area under y=x where x varies from {min_value} to {max_value}'''							)
						print(F'''Estimated value is {estimated_value}'''							)
						print(F'''Expected value is {expected_value}'''							)
						print(F'''Total error is {abs(estimated_value - expected_value							)}'''							)
						print("******************"							)





def      lowerCamelCase_					(   __lowerCAmelCase							)				->   None:




						'''simple docstring'''



						def function_to_integrate(__lowerCAmelCase							) -> float:
												return sqrt(4.0 - x * x							)

						lowerCamelCase__   =area_under_curve_estimator(
						    __lowerCAmelCase  ,       __lowerCAmelCase  ,       0.0  ,       2.0							)

						print("******************"							)
						print("Estimating pi using area_under_curve_estimator"							)
						print(F'''Estimated value is {estimated_value}'''							)
						print(F'''Expected value is {pi}'''							)
						print(F'''Total error is {abs(estimated_value - pi							)}'''							)
						print("******************"							)


if __name__ == "__main__":
	import doctest

	doctest.testmod()


